The number of girls to the number of boys in Primary 6 Patience was 3 : 4. The number of girls to the number of boys in Primary 6 Gentleness was 4 : 5. Both classes had the same number of girls. When 6 boys from Primary 6 Patience joined Primary 6 Gentleness, the ratio of the number of girls to the number of boys in Primary 6 Patience became 6 : 7. Find the total enrolment of both classes.

Primary 6 Patience		Primary 6 Gentleness
Girls	Boys	Girls	Boys
3x4	4x4	4x3	5x3
1x12		1x12
12 u	16 u	12 u	15 u

The number of girls in both classes is the same.  Make the number of girls the same.  LCM of 3 and 4 is 12.

	Primary 6 Patience		Primary 6 Gentleness
	Girls	Boys	Girls	Boys
Before	12 u	16 u	12 u	15 u
Change		- 6		+ 6
After	6x2 = 12 u	7x2 = 14 u	12 u	15 u + 6

The number of girls in Primary 6 Patience remains unchanged.  Make the number of girls in Primary 6 the same.  LCM of 12 and 6 is 12.

Number of boys from Primary 6 Patience that joined Primary 6 Gentleness
= 16 u - 14 u
= 2 u

2 u = 6

1 u = 6 ÷ 2 = 3

Total enrolment of both classes
= 12 u + 16 u + 12 u + 15 u
= 55 u
= 55 x 3
= 165

Answer(s): 165